ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of TiN (Materials Project id mp-492)

       564      106      106        0        0        0  
       106      564      106        0        0        0  
       106      106      564        0        0        0  
         0        0        0      154        0        0  
         0        0        0        0      154        0  
         0        0        0        0        0      154  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 258.67 GPaEV = 446.2 GPaGV = 184 GPaνV = 0.2125
ReussKR = 258.67 GPaER = 432.81 GPaGR = 177.22 GPaνR = 0.22113
HillKH = 258.67 GPaEH = 439.53 GPaGH = 180.61 GPaνH = 0.2168

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
154 GPa 154 GPa 154 GPa 458 GPa 458 GPa 776 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 385.5 GPa 530.46 GPa 1.2887 TPa–1 1.2887 TPa–1 154 GPa 229 GPa0.12340.34339Value
Anisotropy 1.376 1.0000 1.487 2.7827Anisotropy
Axis 0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
0.0000
-0.7072
0.7071
-0.0002
0.7071
Axis
0.1734
0.9849
-0.0000
-0.7071
-0.0002
-0.7071
-0.0000
1.0000
0.0000
0.7071
-0.0005
-0.7071
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane